Add two numbers represented by linked lists | Set 1

Given two numbers represented by two lists, write a function that returns the sum list. The sum list is list representation of the addition of two input numbers.

Example:

Input:
List1: 5->6->3 // represents number 365
List2: 8->4->2 // represents number 248
Output:
Resultant list: 3->1->6 // represents number 613
Explanation: 365 + 248 = 613

Input:
List1: 7->5->9->4->6 // represents number 64957
List2: 8->4 // represents number 48
Output:
Resultant list: 5->0->0->5->6 // represents number 65005
Explanation: 64957 + 48 = 65005

Approach: Traverse both lists and One by one pick nodes of both lists and add the values. If the sum is more than 10 then make carry as 1 and reduce sum. If one list has more elements than the other then consider remaining values of this list as 0.



The steps are:

  1. Traverse the two linked lists from start to end
  2. Add the two digits each from respective linked lists.
  3. If one of the list has reached the end then take 0 as its digit.
  4. Continue it until both the lists end.
  5. If the sum of two digits is greater than 9 then set carry as and the current digit as sum % 10

Below is the implementation of this approach.

C++

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// C++ program to add two numbers
// represented by linked list
#include <bits/stdc++.h>
using namespace std;
  
/* Linked list node */
class Node {
public:
    int data;
    Node* next;
};
  
/* Function to create a 
new node with given data */
Node* newNode(int data)
{
    Node* new_node = new Node();
    new_node->data = data;
    new_node->next = NULL;
    return new_node;
}
  
/* Function to insert a node at the
beginning of the Singly Linked List */
void push(Node** head_ref, int new_data)
{
    /* allocate node */
    Node* new_node = newNode(new_data);
  
    /* link the old list off the new node */
    new_node->next = (*head_ref);
  
    /* move the head to point to the new node */
    (*head_ref) = new_node;
}
  
/* Adds contents of two linked lists and 
return the head node of resultant list */
Node* addTwoLists(Node* first, Node* second)
{
  
    // res is head node of the resultant list
    Node* res = NULL;
    Node *temp, *prev = NULL;
    int carry = 0, sum;
  
    // while both lists exist
    while (first != NULL
           || second != NULL) {
        // Calculate value of next
        // digit in resultant list.
        // The next digit is sum of
        // following things
        // (i) Carry
        // (ii) Next digit of first
        // list (if there is a next digit)
        // (ii) Next digit of second
        // list (if there is a next digit)
        sum = carry + (first ? first->data : 0)
              + (second ? second->data : 0);
  
        // update carry for next calulation
        carry = (sum >= 10) ? 1 : 0;
  
        // update sum if it is greater than 10
        sum = sum % 10;
  
        // Create a new node with sum as data
        temp = newNode(sum);
  
        // if this is the first node then
        // set it as head of the resultant list
        if (res == NULL)
            res = temp;
  
        // If this is not the first
        // node then connect it to the rest.
        else
            prev->next = temp;
  
        // Set prev for next insertion
        prev = temp;
  
        // Move first and second
        // pointers to next nodes
        if (first)
            first = first->next;
        if (second)
            second = second->next;
    }
  
    if (carry > 0)
        temp->next = newNode(carry);
  
    // return head of the resultant list
    return res;
}
  
// A utility function to print a linked list
void printList(Node* node)
{
    while (node != NULL) {
        cout << node->data << " ";
        node = node->next;
    }
    cout << endl;
}
  
/* Driver code */
int main(void)
{
    Node* res = NULL;
    Node* first = NULL;
    Node* second = NULL;
  
    // create first list 7->5->9->4->6
    push(&first, 6);
    push(&first, 4);
    push(&first, 9);
    push(&first, 5);
    push(&first, 7);
    printf("First List is ");
    printList(first);
  
    // create second list 8->4
    push(&second, 4);
    push(&second, 8);
    cout << "Second List is ";
    printList(second);
  
    // Add the two lists and see result
    res = addTwoLists(first, second);
    cout << "Resultant list is ";
    printList(res);
  
    return 0;
}
  
// This code is contributed by rathbhupendra

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C

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#include <stdio.h>
#include <stdlib.h>
  
/* Linked list node */
struct Node {
    int data;
    struct Node* next;
};
  
/* Function to create a new node with given data */
struct Node* newNode(int data)
{
    struct Node* new_node = (struct Node*)
        malloc(
            sizeof(struct Node));
    new_node->data = data;
    new_node->next = NULL;
    return new_node;
}
  
/* Function to insert a node 
at the beginning of the Singly Linked List */
void push(struct Node** head_ref, int new_data)
{
    /* allocate node */
    struct Node* new_node = newNode(new_data);
  
    /* link the old list off the new node */
    new_node->next = (*head_ref);
  
    /* move the head to point to the new node */
    (*head_ref) = new_node;
}
  
/* Adds contents of two linked
 lists and return the head node
 of resultant list */
struct Node* addTwoLists(
    struct Node* first,
    struct Node* second)
{
  
    // res is head node of the resultant list
    struct Node* res = NULL;
    struct Node *temp, *prev = NULL;
    int carry = 0, sum;
  
    // while both lists exist
    while (first != NULL || second != NULL) {
        // Calculate value of next
        // digit in resultant list.
        // The next digit is sum
        // of following things
        // (i)  Carry
        // (ii) Next digit of first
        // list (if there is a next digit)
        // (ii) Next digit of second
        // list (if there is a next digit)
        sum = carry + (first ? first->data : 0)
              + (second ? second->data : 0);
  
        // Update carry for next calulation
        carry = (sum >= 10) ? 1 : 0;
  
        // Update sum if it is greater than 10
        sum = sum % 10;
  
        // Create a new node with sum as data
        temp = newNode(sum);
  
        // if this is the first node then
        // set it as head of the resultant list
        if (res == NULL)
            res = temp;
        // If this is not the first node
        // then connect it to the rest.
        else
            prev->next = temp;
  
        // Set prev for next insertion
        prev = temp;
  
        // Move first and second
        // pointers to next nodes
        if (first)
            first = first->next;
        if (second)
            second = second->next;
    }
  
    if (carry > 0)
        temp->next = newNode(carry);
  
    // return head of the resultant list
    return res;
}
  
// A utility function to print a linked list
void printList(struct Node* node)
{
    while (node != NULL) {
        printf("%d ", node->data);
        node = node->next;
    }
    printf("\n");
}
  
/* Driver program to test above function */
int main(void)
{
    struct Node* res = NULL;
    struct Node* first = NULL;
    struct Node* second = NULL;
  
    // create first list 7->5->9->4->6
    push(&first, 6);
    push(&first, 4);
    push(&first, 9);
    push(&first, 5);
    push(&first, 7);
    printf("First List is ");
    printList(first);
  
    // create second list 8->4
    push(&second, 4);
    push(&second, 8);
    printf("Second List is ");
    printList(second);
  
    // Add the two lists and see result
    res = addTwoLists(first, second);
    printf("Resultant list is ");
    printList(res);
  
    return 0;
}

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Java

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// Java program to add two numbers
// represented by linked list
  
class LinkedList {
  
    static Node head1, head2;
  
    static class Node {
  
        int data;
        Node next;
  
        Node(int d)
        {
            data = d;
            next = null;
        }
    }
  
    /* Adds contents of two linked 
lists and return the head node 
of resultant list */
    Node addTwoLists(Node first, Node second)
    {
        // res is head node of the resultant list
        Node res = null;
        Node prev = null;
        Node temp = null;
        int carry = 0, sum;
  
        // while both lists exist
        while (first != null || second != null) {
            // Calculate value of next
            // digit in resultant list.
            // The next digit is sum
            // of following things
            // (i)  Carry
            // (ii) Next digit of first
            // list (if there is a next digit)
            // (ii) Next digit of second
            // list (if there is a next digit)
            sum = carry + (first != null ? first.data : 0)
                  + (second != null ? second.data : 0);
  
            // update carry for next calulation
            carry = (sum >= 10) ? 1 : 0;
  
            // update sum if it is greater than 10
            sum = sum % 10;
  
            // Create a new node with sum as data
            temp = new Node(sum);
  
            // if this is the first node then set
            // it as head of the resultant list
            if (res == null) {
                res = temp;
            }
  
            // If this is not the first
            // node then connect it to the rest.
            else {
                prev.next = temp;
            }
  
            // Set prev for next insertion
            prev = temp;
  
            // Move first and second pointers
            // to next nodes
            if (first != null) {
                first = first.next;
            }
            if (second != null) {
                second = second.next;
            }
        }
  
        if (carry > 0) {
            temp.next = new Node(carry);
        }
  
        // return head of the resultant list
        return res;
    }
    /* Utility function to print a linked list */
  
    void printList(Node head)
    {
        while (head != null) {
            System.out.print(head.data + " ");
            head = head.next;
        }
        System.out.println("");
    }
  
    public static void main(String[] args)
    {
        LinkedList list = new LinkedList();
  
        // creating first list
        list.head1 = new Node(7);
        list.head1.next = new Node(5);
        list.head1.next.next = new Node(9);
        list.head1.next.next.next = new Node(4);
        list.head1.next.next.next.next = new Node(6);
        System.out.print("First List is ");
        list.printList(head1);
  
        // creating seconnd list
        list.head2 = new Node(8);
        list.head2.next = new Node(4);
        System.out.print("Second List is ");
        list.printList(head2);
  
        // add the two lists and see the result
        Node rs = list.addTwoLists(head1, head2);
        System.out.print("Resultant List is ");
        list.printList(rs);
    }
}
  
// this code has been contributed by Mayank Jaiswal

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Python

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# Python program to add two numbers represented by linked list
  
# Node class
class Node:
  
    # Constructor to initialize the node object
    def __init__(self, data):
        self.data = data
        self.next = None
  
class LinkedList:
  
    # Function to initialize head
    def __init__(self):
        self.head = None
  
    # Function to insert a new node at the beginning
    def push(self, new_data):
        new_node = Node(new_data)
        new_node.next = self.head
        self.head = new_node
  
    # Add contents of two linked lists and return the head
    # node of resultant list
    def addTwoLists(self, first, second):
        prev = None
        temp = None
        carry = 0 
  
        # While both list exists
        while(first is not None or second is not None):
  
            # Calculate the value of next digit in
            # resultant list
            # The next digit is sum of following things
            # (i) Carry
            # (ii) Next digit of first list (if ther is a
            # next digit)
            # (iii) Next digit of second list ( if there
            # is a next digit)
            fdata = 0 if first is None else first.data
            sdata = 0 if second is None else second.data
            Sum = carry + fdata + sdata
  
            # update carry for next calculation
            carry = 1 if Sum >= 10 else 0
  
            # update sum if it is greater than 10
            Sum = Sum if Sum < 10 else Sum % 10
  
            # Create a new node with sum as data
            temp = Node(Sum)
  
            # if this is the first node then set it as head
            # of resultant list
            if self.head is None:
                self.head = temp
            else :
                prev.next = temp 
  
            # Set prev for next insertion
            prev = temp
  
            # Move first and second pointers to next nodes
            if first is not None:
                first = first.next
            if second is not None:
                second = second.next
  
        if carry > 0:
            temp.next = Node(carry)
  
    # Utility function to print the linked LinkedList
    def printList(self):
        temp = self.head
        while(temp):
            print temp.data,
            temp = temp.next
  
# Driver program to test above function
first = LinkedList()
second = LinkedList()
  
# Create first list
first.push(6)
first.push(4)
first.push(9)
first.push(5)
first.push(7)
print "First List is ",
first.printList()
  
# Create second list
second.push(4)
second.push(8)
print "\nSecond List is ",
second.printList()
  
# Add the two lists and see result
res = LinkedList()
res.addTwoLists(first.head, second.head)
print "\nResultant list is ",
res.printList()
  
# This code is contributed by Nikhil Kumar Singh(nickzuck_007)

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C#

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// C# program to add two numbers
// represented by linked list
using System;
  
public class LinkedList {
  
    Node head1, head2;
  
    public class Node {
        public int data;
        public Node next;
  
        public Node(int d)
        {
            data = d;
            next = null;
        }
    }
  
    /* Adds contents of two linked lists 
    and return the head node of resultant list */
    Node addTwoLists(Node first, Node second)
    {
        // res is head node of the resultant list
        Node res = null;
        Node prev = null;
        Node temp = null;
        int carry = 0, sum;
  
        // while both lists exist
        while (first != null || second != null) {
            // Calculate value of next digit in resultant list.
            // The next digit is sum of following things
            // (i) Carry
            // (ii) Next digit of first list (if there is a next digit)
            // (ii) Next digit of second list (if there is a next digit)
            sum = carry + (first != null ? first.data : 0)
                  + (second != null ? second.data : 0);
  
            // update carry for next calulation
            carry = (sum >= 10) ? 1 : 0;
  
            // update sum if it is greater than 10
            sum = sum % 10;
  
            // Create a new node with sum as data
            temp = new Node(sum);
  
            // if this is the first node then set it as head of
            // the resultant list
            if (res == null) {
                res = temp;
            }
  
            // If this is not the first
            // node then connect it to the rest.
            else {
                prev.next = temp;
            }
  
            // Set prev for next insertion
            prev = temp;
  
            // Move first and second pointers to next nodes
            if (first != null) {
                first = first.next;
            }
            if (second != null) {
                second = second.next;
            }
        }
  
        if (carry > 0) {
            temp.next = new Node(carry);
        }
  
        // return head of the resultant list
        return res;
    }
    /* Utility function to print a linked list */
  
    void printList(Node head)
    {
        while (head != null) {
            Console.Write(head.data + " ");
            head = head.next;
        }
        Console.WriteLine("");
    }
  
    // Driver code
    public static void Main(String[] args)
    {
        LinkedList list = new LinkedList();
  
        // creating first list
        list.head1 = new Node(7);
        list.head1.next = new Node(5);
        list.head1.next.next = new Node(9);
        list.head1.next.next.next = new Node(4);
        list.head1.next.next.next.next = new Node(6);
        Console.Write("First List is ");
        list.printList(list.head1);
  
        // creating seconnd list
        list.head2 = new Node(8);
        list.head2.next = new Node(4);
        Console.Write("Second List is ");
        list.printList(list.head2);
  
        // add the two lists and see the result
        Node rs = list.addTwoLists(list.head1, list.head2);
        Console.Write("Resultant List is ");
        list.printList(rs);
    }
}
  
// This code contributed by Rajput-Ji

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Output:

  First List is 7 5 9 4 6
  Second List is 8 4
  Resultant list is 5 0 0 5 6

Complexity Analysis:

  • Time Complexity: O(m + n), where m and n are number of nodes in first and second lists respectively.
    The lists needs to be traversed only once.
  • Space Complexity: O(m + n).
    A temporary linked list is needed to store the output number.

Related Article: Add two numbers represented by linked lists | Set 2

Please write comments if you find the above codes/algorithms incorrect, or find other ways to solve the same problem.

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